Right half-plane
= Right half-plane
{title2=$\{z\in\mathbb C:\operatorname{Re}z>0\}$}
The <right half-plane> consists of <complex numbers> with positive <real part>. Its <boundary> is the imaginary axis. For example, $1+i$ is inside, $i$ is on the <boundary>, and $-1+i$ is outside. Rotation $z\mapsto iz$ takes the <right half-plane> onto the <upper half-plane>; the <Cayley transform between the half-plane and disk> uses $R(z)=(z-1)/(z+1)$ for this convention.